{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will use Gated Recurrent Units to develop time series forecasting models.\n",
    "The dataset used for the examples of this notebook is on air pollution measured by concentration of\n",
    "particulate matter (PM) of diameter less than or equal to 2.5 micrometers. There are other variables\n",
    "such as air pressure, air temparature, dewpoint and so on.\n",
    "Two time series models are developed - one on air pressure and the other on pm2.5.\n",
    "The dataset has been downloaded from UCI Machine Learning Repository.\n",
    "https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import sys\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#set current working directory\n",
    "os.chdir('D:/Practical Time Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Read the dataset into a pandas.DataFrame\n",
    "df = pd.read_csv('datasets/PRSA_data_2010.1.1-2014.12.31.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the dataframe: (43824, 13)\n"
     ]
    }
   ],
   "source": [
    "print('Shape of the dataframe:', df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>4.92</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>6.71</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>9.84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-20</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1018.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>12.97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd    Iws  Is  Ir\n",
       "0   1  2010      1    1     0    NaN   -21 -11.0  1021.0   NW   1.79   0   0\n",
       "1   2  2010      1    1     1    NaN   -21 -12.0  1020.0   NW   4.92   0   0\n",
       "2   3  2010      1    1     2    NaN   -21 -11.0  1019.0   NW   6.71   0   0\n",
       "3   4  2010      1    1     3    NaN   -21 -14.0  1019.0   NW   9.84   0   0\n",
       "4   5  2010      1    1     4    NaN   -20 -12.0  1018.0   NW  12.97   0   0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see the first five rows of the DataFrame\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Rows having NaN values in column pm2.5 are dropped.\n",
    "\"\"\"\n",
    "df.dropna(subset=['pm2.5'], axis=0, inplace=True)\n",
    "df.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that the rows are in the right order of date and time of observations,\n",
    "a new column datetime is created from the date and time related columns of the DataFrame.\n",
    "The new column consists of Python's datetime.datetime objects. The DataFrame is sorted in ascending order\n",
    "over this column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df['datetime'] = df[['year', 'month', 'day', 'hour']].apply(lambda row: datetime.datetime(year=row['year'], month=row['month'], day=row['day'],\n",
    "                                                                                          hour=row['hour']), axis=1)\n",
    "df.sort_values('datetime', ascending=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2263f5a3240>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263b7ee240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us draw a box plot to visualize the central tendency and dispersion of PRES\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.boxplot(df['pm2.5'])\n",
    "g.set_title('Box plot of pm2.5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2263f61e828>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NyyLEHqjJH9Hm1i/XHE3PAwCUiWVOjoQQQszj1kmbEEKEhpI2IXxH9SNECyVtQggREEra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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263f58a780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'])\n",
    "g.set_title('Time series of pm2.5')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2263f7ef390>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qoj5z5kyUlpYiKSkJTqcT69evx4kTJ/DCC9U7w4PwL2WOMpQ5yvC/U+tCRtQ7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\nQghhIFLqQghhIFLqQghhIFLqQghhIP8DQgzCTfj3tJIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263f5e6940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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O1hBcvHgxSktLMWzYMPzjH/8AIH2JyJfM7/ejsbERgUAAxcXF8vP8fj8CgYCp1ygrK06/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\nTqETtAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263f62a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's plot the series for six months to check if any pattern apparently exists.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'].loc[df['datetime']<=datetime.datetime(year=2010,month=6,day=30)], color='g')\n",
    "g.set_title('pm2.5 during 2010')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')\n",
    "\n",
    "#Let's zoom in on one month.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'].loc[df['datetime']<=datetime.datetime(year=2010,month=1,day=31)], color='g')\n",
    "g.set_title('pm2.5 during Jan 2010')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent algorithms perform better (for example converge faster) if the variables are wihtin range [-1, 1]. Many sources relax the boundary to even [-3, 3]. The pm2.5 variable is mixmax scaled to bound the tranformed variable within [0,1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "df['scaled_pm2.5'] = scaler.fit_transform(np.array(df['pm2.5']).reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Before training the model, the dataset is split in two parts - train set and validation set.\n",
    "The neural network is trained on the train set. This means computation of the loss function, back propagation\n",
    "and weights updated by a gradient descent algorithm is done on the train set. The validation set is\n",
    "used to evaluate the model and to determine the number of epochs in model training. Increasing the number of \n",
    "epochs will further decrease the loss function on the train set but might not neccesarily have the same effect\n",
    "for the validation set due to overfitting on the train set.Hence, the number of epochs is controlled by keeping\n",
    "a tap on the loss function computed for the validation set. We use Keras with Tensorflow backend to define and train\n",
    "the model. All the steps involved in model training and validation is done by calling appropriate functions\n",
    "of the Keras API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train: (33096, 15)\n",
      "Shape of test: (8661, 15)\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Let's start by splitting the dataset into train and validation. The dataset's time period if from\n",
    "Jan 1st, 2010 to Dec 31st, 2014. The first fours years - 2010 to 2013 is used as train and\n",
    "2014 is kept for validation.\n",
    "\"\"\"\n",
    "split_date = datetime.datetime(year=2014, month=1, day=1, hour=0)\n",
    "df_train = df.loc[df['datetime']<split_date]\n",
    "df_val = df.loc[df['datetime']>=split_date]\n",
    "print('Shape of train:', df_train.shape)\n",
    "print('Shape of test:', df_val.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_pm2.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>-16</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 00:00:00</td>\n",
       "      <td>0.129779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>26</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>148.0</td>\n",
       "      <td>-15</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>2.68</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 01:00:00</td>\n",
       "      <td>0.148893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>159.0</td>\n",
       "      <td>-11</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>3.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 02:00:00</td>\n",
       "      <td>0.159960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>181.0</td>\n",
       "      <td>-7</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1022.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>5.36</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 03:00:00</td>\n",
       "      <td>0.182093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>29</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>138.0</td>\n",
       "      <td>-7</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1022.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>6.25</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 04:00:00</td>\n",
       "      <td>0.138833</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd   Iws  Is  Ir  \\\n",
       "0  25  2010      1    2     0  129.0   -16  -4.0  1020.0   SE  1.79   0   0   \n",
       "1  26  2010      1    2     1  148.0   -15  -4.0  1020.0   SE  2.68   0   0   \n",
       "2  27  2010      1    2     2  159.0   -11  -5.0  1021.0   SE  3.57   0   0   \n",
       "3  28  2010      1    2     3  181.0    -7  -5.0  1022.0   SE  5.36   1   0   \n",
       "4  29  2010      1    2     4  138.0    -7  -5.0  1022.0   SE  6.25   2   0   \n",
       "\n",
       "             datetime  scaled_pm2.5  \n",
       "0 2010-01-02 00:00:00      0.129779  \n",
       "1 2010-01-02 01:00:00      0.148893  \n",
       "2 2010-01-02 02:00:00      0.159960  \n",
       "3 2010-01-02 03:00:00      0.182093  \n",
       "4 2010-01-02 04:00:00      0.138833  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of train\n",
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_pm2.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33096</th>\n",
       "      <td>35065</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1014.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>143.48</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 00:00:00</td>\n",
       "      <td>0.024145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33097</th>\n",
       "      <td>35066</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>53.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>147.50</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 01:00:00</td>\n",
       "      <td>0.053320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33098</th>\n",
       "      <td>35067</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>65.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>151.52</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 02:00:00</td>\n",
       "      <td>0.065392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33099</th>\n",
       "      <td>35068</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>70.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>153.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 03:00:00</td>\n",
       "      <td>0.070423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33100</th>\n",
       "      <td>35069</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>79.0</td>\n",
       "      <td>-18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1012.0</td>\n",
       "      <td>cv</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 04:00:00</td>\n",
       "      <td>0.079477</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd     Iws  \\\n",
       "33096  35065  2014      1    1     0   24.0   -20   7.0  1014.0   NW  143.48   \n",
       "33097  35066  2014      1    1     1   53.0   -20   7.0  1013.0   NW  147.50   \n",
       "33098  35067  2014      1    1     2   65.0   -20   6.0  1013.0   NW  151.52   \n",
       "33099  35068  2014      1    1     3   70.0   -20   6.0  1013.0   NW  153.31   \n",
       "33100  35069  2014      1    1     4   79.0   -18   3.0  1012.0   cv    0.89   \n",
       "\n",
       "       Is  Ir            datetime  scaled_pm2.5  \n",
       "33096   0   0 2014-01-01 00:00:00      0.024145  \n",
       "33097   0   0 2014-01-01 01:00:00      0.053320  \n",
       "33098   0   0 2014-01-01 02:00:00      0.065392  \n",
       "33099   0   0 2014-01-01 03:00:00      0.070423  \n",
       "33100   0   0 2014-01-01 04:00:00      0.079477  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of validation\n",
    "df_val.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Reset the indices of the validation set\n",
    "df_val.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2264046d2e8>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kuVyO3377DfPnz8elS5e03lu2bBnngRH7kcsdHYHpzG1DPnWKeldwLS+Psqut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\nSYH4ARvN5k2+Y78FAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263ffdc400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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1VqxduxZXr14FwzBVL+WmUiVFlRqFojuMs5x/h2/qtHZtmQ8eBOBJT1vlFfIf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2263ffeec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The train and validation time series of scaled_pm2.5 is also plotted.\n",
    "\"\"\"\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_train['scaled_pm2.5'], color='b')\n",
    "g.set_title('Time series of scaled pm2.5 in train set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled pm2.5 readings')\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_val['scaled_pm2.5'], color='r')\n",
    "g.set_title('Time series of scaled pm2.5 in validation set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled pm2.5 readings')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to generate regressors (X) and target variable (y) for train and validation. 2-D array of regressor and 1-D array of target is created from the original 1-D array of columm standardized_pm2.5 in the DataFrames. For the time series forecasting model, Past seven days of observations are used to predict for the next day. This is equivalent to a AR(7) model. We define a function which takes the original time series and the number of timesteps in regressors as input to generate the arrays of X and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def makeXy(ts, nb_timesteps):\n",
    "    \"\"\"\n",
    "    Input: \n",
    "           ts: original time series\n",
    "           nb_timesteps: number of time steps in the regressors\n",
    "    Output: \n",
    "           X: 2-D array of regressors\n",
    "           y: 1-D array of target \n",
    "    \"\"\"\n",
    "    X = []\n",
    "    y = []\n",
    "    for i in range(nb_timesteps, ts.shape[0]):\n",
    "        X.append(list(ts.loc[i-nb_timesteps:i-1]))\n",
    "        y.append(ts.loc[i])\n",
    "    X, y = np.array(X), np.array(y)\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train arrays: (33089, 7) (33089,)\n"
     ]
    }
   ],
   "source": [
    "X_train, y_train = makeXy(df_train['scaled_pm2.5'], 7)\n",
    "print('Shape of train arrays:', X_train.shape, y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of validation arrays: (8654, 7) (8654,)\n"
     ]
    }
   ],
   "source": [
    "X_val, y_val = makeXy(df_val['scaled_pm2.5'], 7)\n",
    "print('Shape of validation arrays:', X_val.shape, y_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input to RNN layers must be of shape (number of samples, number of timesteps, number of features per timestep). In this case we are modeling only pm2.5 hence number of features per timestep is one. Number of timesteps is seven and number of samples is same as the number of samples in X_train and X_val, which are reshaped to 3D arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of arrays after reshaping: (33089, 7, 1) (8654, 7, 1)\n"
     ]
    }
   ],
   "source": [
    "#X_train and X_val are reshaped to 3D arrays\n",
    "X_train, X_val = X_train.reshape((X_train.shape[0], X_train.shape[1], 1)), X_val.reshape((X_val.shape[0], X_val.shape[1], 1))\n",
    "print('Shape of arrays after reshaping:', X_train.shape, X_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define the MLP using the Keras Functional API. In this approach a layer can be declared as the input of the following layer at the time of defining the next layer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.layers import Dense, Input, Dropout\n",
    "from keras.layers.recurrent import GRU\n",
    "from keras.optimizers import SGD\n",
    "from keras.models import Model\n",
    "from keras.models import load_model\n",
    "from keras.callbacks import ModelCheckpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Define input layer which has shape (None, 7) and of type float32. None indicates the number of instances\n",
    "input_layer = Input(shape=(7,1), dtype='float32')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The GRU layers are defined for seven timesteps. In this example, two GRU layers are stacked. The first GRU returns the output from each all seven timesteps. This output is a sequence and is fed to the second GRU which returns output only from the last step. The first GRU has sixty four hidden neurons in each timestep. Hence the sequence returned by the first GRU has sixty four features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gru_layer1 = GRU(64, input_shape=(7,1), return_sequences=True)(input_layer)\n",
    "gru_layer2 = GRU(32, input_shape=(7,64), return_sequences=False)(gru_layer1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dropout_layer = Dropout(0.2)(gru_layer2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Finally the output layer gives prediction for the next day's air pressure.\n",
    "output_layer = Dense(1, activation='linear')(dropout_layer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input, dense and output layers will now be packed inside a Model, which is wrapper class for training and making\n",
    "predictions. The box plot of pm2.5 shows the presence of outliers. Hence, mean absolute error (MAE) is used as absolute deviations suffer less fluctuations compared to squared deviations.\n",
    "\n",
    "The network's weights are optimized by the Adam algorithm. Adam stands for adaptive moment estimation\n",
    "and has been a popular choice for training deep neural networks. Unlike, stochastic gradient descent, adam uses\n",
    "different learning rates for each weight and separately updates the same as the training progresses. The learning rate of a weight is updated based on exponentially weighted moving averages of the weight's gradients and the squared gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_1 (InputLayer)         (None, 7, 1)              0         \n",
      "_________________________________________________________________\n",
      "gru_1 (GRU)                  (None, 7, 64)             12672     \n",
      "_________________________________________________________________\n",
      "gru_2 (GRU)                  (None, 32)                9312      \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 32)                0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 33        \n",
      "=================================================================\n",
      "Total params: 22,017\n",
      "Trainable params: 22,017\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "ts_model = Model(inputs=input_layer, outputs=output_layer)\n",
    "ts_model.compile(loss='mean_absolute_error', optimizer='adam')\n",
    "ts_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is trained by calling the fit function on the model object and passing the X_train and y_train. The training \n",
    "is done for a predefined number of epochs. Additionally, batch_size defines the number of samples of train set to be\n",
    "used for a instance of back propagation.The validation dataset is also passed to evaluate the model after every epoch\n",
    "completes. A ModelCheckpoint object tracks the loss function on the validation set and saves the model for the epoch,\n",
    "at which the loss function has been minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 33089 samples, validate on 8654 samples\n",
      "Epoch 1/20\n",
      "33089/33089 [==============================] - 22s - loss: 0.0171 - val_loss: 0.0117\n",
      "Epoch 2/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0152 - val_loss: 0.0119\n",
      "Epoch 3/20\n",
      "33089/33089 [==============================] - 22s - loss: 0.0151 - val_loss: 0.0133\n",
      "Epoch 4/20\n",
      "33089/33089 [==============================] - 24s - loss: 0.0150 - val_loss: 0.0127\n",
      "Epoch 5/20\n",
      "33089/33089 [==============================] - 26s - loss: 0.0149 - val_loss: 0.0125\n",
      "Epoch 6/20\n",
      "33089/33089 [==============================] - 24s - loss: 0.0150 - val_loss: 0.0119\n",
      "Epoch 7/20\n",
      "33089/33089 [==============================] - 25s - loss: 0.0149 - val_loss: 0.0118\n",
      "Epoch 8/20\n",
      "33089/33089 [==============================] - 25s - loss: 0.0149 - val_loss: 0.0122\n",
      "Epoch 9/20\n",
      "33089/33089 [==============================] - 24s - loss: 0.0149 - val_loss: 0.0118\n",
      "Epoch 10/20\n",
      "33089/33089 [==============================] - 22s - loss: 0.0148 - val_loss: 0.0121\n",
      "Epoch 11/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0147 - val_loss: 0.0117\n",
      "Epoch 12/20\n",
      "33089/33089 [==============================] - 22s - loss: 0.0148 - val_loss: 0.0122\n",
      "Epoch 13/20\n",
      "33089/33089 [==============================] - 21s - loss: 0.0147 - val_loss: 0.0120\n",
      "Epoch 14/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0148 - val_loss: 0.0118\n",
      "Epoch 15/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0148 - val_loss: 0.0117\n",
      "Epoch 16/20\n",
      "33089/33089 [==============================] - 21s - loss: 0.0148 - val_loss: 0.0116\n",
      "Epoch 17/20\n",
      "33089/33089 [==============================] - 26s - loss: 0.0147 - val_loss: 0.0117\n",
      "Epoch 18/20\n",
      "33089/33089 [==============================] - 28s - loss: 0.0147 - val_loss: 0.0122\n",
      "Epoch 19/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0147 - val_loss: 0.0117\n",
      "Epoch 20/20\n",
      "33089/33089 [==============================] - 23s - loss: 0.0147 - val_loss: 0.0117\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x2268515c9e8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_weights_at = os.path.join('keras_models', 'PRSA_data_PM2.5_GRU_weights.{epoch:02d}-{val_loss:.4f}.hdf5')\n",
    "save_best = ModelCheckpoint(save_weights_at, monitor='val_loss', verbose=0,\n",
    "                            save_best_only=True, save_weights_only=False, mode='min',\n",
    "                            period=1)\n",
    "ts_model.fit(x=X_train, y=y_train, batch_size=16, epochs=20,\n",
    "             verbose=1, callbacks=[save_best], validation_data=(X_val, y_val),\n",
    "             shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction are made for the pm2.5 from the best saved model. The model's predictions, which are on the standardized  pm2.5, are inverse transformed to get predictions of original pm2.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_model = load_model(os.path.join('keras_models', 'PRSA_data_PM2.5_GRU_weights.15-0.0116.hdf5'))\n",
    "preds = best_model.predict(X_val)\n",
    "pred_pm25 = scaler.inverse_transform(preds)\n",
    "pred_pm25 = np.squeeze(pred_pm25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for the validation set: 11.5598\n"
     ]
    }
   ],
   "source": [
    "mae = mean_absolute_error(df_val['pm2.5'].loc[7:], pred_pm25)\n",
    "print('MAE for the validation set:', round(mae, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iqUvMWzYD4Ordxxjbs0fF5Vbp3ln3RVtW/wDAqFFuund38+WXZrKzlYafbCPTpMXZboeN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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x226878de860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's plot the first 50 actual and predicted values of pm2.5.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "plt.plot(range(50), df_val['pm2.5'].loc[7:56], linestyle='-', marker='*', color='r')\n",
    "plt.plot(range(50), pred_pm25[:50], linestyle='-', marker='.', color='b')\n",
    "plt.legend(['Actual','Predicted'], loc=2)\n",
    "plt.title('Actual vs Predicted pm2.5')\n",
    "plt.ylabel('pm2.5')\n",
    "plt.xlabel('Index')\n",
    "plt.savefig('plots/ch5/B07887_05_12.png', format='png', dpi=300)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
